The author is correct that checking if two functions having infinite domains are equal is often impossible. He also has correct statements of some mathematical

The author is correct that checking if two functions having infinite domains are equal is often impossible. He also has correct statements of some mathematical theorems. But people in this thread have provided counterexamples to his claim. That means he needs to fix the mistakes he made. If you are interested in what serious mathematicians have to say on this topic see https://homotopytypetheory.org/ https://homotopytypetheory.org/.